úÎ!źŒ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz { | } ~  €  ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Implements tensor index.(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX Safe &'17=>?@AX_Č  multilinear7Generic index type finitely- or infinitely-dimensional  multilinearYTensor index class which may be lower (covariant), upper (contravariant) or indifferent.  multilinear Index name  multilinear=Returns True if index is lower (covariant), False otherwise.  multilinearAReturns True if index is upper (contravariant), False otherwise.  multilinear7Returns True if index if indifferent, False otherwise.  multilineareReturns True if two indices are equivalent, thus differs only by name, but share same size and type.  multilinearInfix equivalent for equiv. Has low priority equal to 2.  multilinearConvert to generic index type  multilinear.Indices can be compared by its name and size |<Used to allow to put tensors to typical ordered containers | multilinearShow tensor index  multilinear-Finite index is a Multilinear.Index instance    2A (multi)linear algbra library.(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_aŔ" multilinear‰If container on which tensor instance is built, allows for random access of its elements, then the tensor can be instanced as Accessible  multilinearAccessing tensor elements el ["i","j"] t [4,5]) returns all tensor elements which index i is equal to 4 and index jB is equal to 5. Values of other indices are insignificant ‹If given index value is out of range, then modulo operation is performed: el ["i","j"] t [40 50] = t[40 mod size i, 50 mod size j]  multilinearInfix equivalent for el  multilinear;Multidimensional array treated as multilinear map - tensor  multilinear Add scalar a to each element of tensor t  multilinear Subtract each element of tensor t from scalar scalar left  multilinearMultiply scalar a by each element of tensor t  multilinearAdd each element of tensor t to scalar a  multilinearSubtract scalar a from each element of tensor t  multilinear Multiply each element of tensor t by scalar a  multilinearList of all tensor indices  multilinearList of tensor indices names  multilinear=Tensor order - number of covariant and contravariant indices order t = (cv, cov) where cv is number of upper and cov is number of lower indices  multilinear%Return size of index with given name ! multilinearKCheck if tensors are equivalent (have same indices but in different order) " multilinearInfix equivalent of ! . Has low priority equal to 1. |# multilineart $| "ij" "kl"! renames upper indices of tensor t to ij and lower indices to kl $ multilinear raise t "i" raises an index i of tensor t % multilinearInfix equivalent of $ & multilinear lower t "i" lowers an index i of tensor t ' multilinearInfix equivalent of & ( multilinearSwitch all indices of tensor t. - upper indices becomes lower and vice versa ) multilinearShift tensor index right shiftRight t "i" moves index i of tensor tl one level depeer in recursion. Elements of tensor as indexed with indices names becomes unchanged. RRight shift of an index is equivalent to left shift of its successor in recursion s , if only s exists, so: Given a tensor t[i1,i2,i3,...]: 8shiftRight t "i2" == t[i1,i3,i2,...] == shiftLeft t "i3"* multilinearInfix equivalent of )  t |>> "i" moves index i of tensor t one level depeer in recursion + multilinearShift tensor index rightmost shiftRightmost t "i" moves index i of tensor tq to the deepest level in recursion. Elements of tensor as indexed with indices names becomes unchanged. , multilinearInfix equivalent of +  t |>>> "i" moves index i of tensor t# to the deepest level in recursion - multilinear]Shift tensor index left. Elements of tensor as indexed with indices names becomes unchanged. shiftLeft t "i" moves index i of tensor t one level up in recursion TLeft shift of an index is equivalent to right shift of its predecessor in recursion p , if only p. exists, so: Given a tensor t[i1,i2,i3,...]: 8shiftLeft t "i3" == t[i1,i3,i2,...] == shiftRight t "i2". multilinearInfix equivalent to -  t <<| "i" moves index i of tensor t one level up in recursion / multilinearaShift tensor index leftmost. Elements of tensor as indexed with indices names becomes unchanged. shiftLeftmost t "i" moves index i of tensor t! to the first level in recursion 0 multilinearInfix equivalent of /  t <<<| "i" moves index i of tensor t! to the first level in recursion 1 multilinearSimple mapping map f t returns tensor t2 in which t2[i1,i2,...] = f t[i1,i2,...] 2 multilinear˙ôFiltering tensor. Filtering multi-dimensional arrray may be dangerous, as we always assume, that on each recursion level, all tensors have the same size (length). To disable invalid filters, filtering is done over indices, not tensor elements. Filter function takes and index name and index value and if it returns True, this index value remains in result tensor. This allows to remove whole columns or rows of eg. a matrix: filter (i n -> i == "a" || i > 10) filters all rows of "a" index (because if i ţ= "a", filter returns True) and for "a" index filter elements with index value <= 10 But this disallow to remove particular matrix element. If for some index all elements are removed, the index itself is removed from tensor. 3 multilinearFiltering one index of tensor. 4 multilinear#Zip tensors with binary combinator 2 multilinearfilter function multilineartensor to filter3 multilinearIndex name to filter multilinearfilter function multilineartensor to filter"214( #!"$%&')-*+,./03"214( #!"$%&')-*+,./037445445"1#9 %8'8*6,6.606 A (multi)linear algbra library.(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_fB"214( #!"$%&')-*+,./03 Finite-dimensional tensor index.(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX Safe &'17=>?@AX_mŻ5 multilinear7Index of finite-dimensional tensor with specified size < multilinear.Indices can be compared by its name and size |<Used to allow to put tensors to typical ordered containers |= multilinear-Finite index is a Multilinear.Index instance > multilinearShow instance of Finite index 57689:57689:Generic array tensor(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_ĄOA multilinear>Tensor defined recursively as scalar or list of other tensors c is type of a container, i is type of index size and a is type of tensor elements B multilinearScalar C multilinear&Simple, one-dimensional finite tensor D multilinearFinite array of other tensors F multilinear Finite index Mutltilinear.Index.Finite of tensor H multilinear+Array of tensors on deeper recursion level Œ multilinearERROR MESSAGE  multilinearERROR MESSAGE Ž multilinearERROR MESSAGE  multilinearERROR MESSAGE I multilinear"Return true if tensor is a scalar J multilinear)Return true if tensor is a simple tensor K multilinear*Return True if tensor is a complex tensor L multilinearReturn generic tensor index  multilineargReturns sample tensor on deeper recursion level.Used to determine some features common for all tensors M multilinear&Recursive indexing on list tensor  t ! i = t[i] N multilinear3move contravariant indices to lower recursion level‘ multilinearQMerge FiniteTensor of Scalars to SimpleFinite tensor for performance improvement ’ multilinear@Generic map function, which does not require a,b types to be Num“ multilinearrApply a tensor operator (here denoted by (+) ) elem by elem, trying to connect as many common indices as possible O multilinearSApply a tensor operator elem by elem and merge scalars to simple tensor at the and ” multilinearLZipping two tensors with a combinator, assuming they have the same indices. • multilinear zipT errorP multilineardot product of two tensorsQ multilinearcontraction error– multilinear™Transpose Vector of Vectors, analogous to Data.List.transpose function. It is assumed, that all vectors on deeper recursion level have the same length. R multilinear1List allows for random access to tensor elements U multilinear$Tensors can be divided by each otherV multilinear2Tensors can be added, subtracted and multiplicatedW multilinear Print tensorX multilinearNFData instanceM multilineartensor t multilinearindex i multilineartensor t[i]“ multilinearFirst argument of operator multilinearSecond argument of operator multilinear4Operator on tensor elements if indices are different multilinear.Tensor operator called if indices are the same multilinear Result tensorO multilinearFirst argument of operator multilinearSecond argument of operator multilinear4Operator on tensor elements if indices are different multilinear.Tensor operator called if indices are the same multilinear Result tensor” multilinearThe zipping combinator multilinearFirst tensor to zip multilinearSecond tensor to zip multilinear Result tensor• multilinear-zipT function variant where the error occured multilinear$Index of first dot product parameter multilinear%Index of second dot product parameter multilinear Erorr messageP multilinearFirst dot product argument multilinearSecond dot product argument multilinearResulting dot productQ multilinear(dot function variant where error occured multilinear$Index of first dot product parameter multilinear%Index of second dot product parameter multilinear Erorr message– multilinearVector of vectors to transposeABCDEFGHIJKLMNOPQABCDEFGHMIJKPOQLN"Infinite-dimensional tensor index.(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX Safe &'17=>?@AX_ŚŞ[ multilinear%Index of infinite-dimensional tensor a multilinear/Infinite index is a Multilinear.Index instance b multilinear Show instance of Infinite index []\^_[]\^_:Tensors constructors (finitely- or infinitely-dimensional)(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_ęUe multilinear,Generate tensor as functions of its indices f multilinear*Generate tensor composed of other tensors g multilinear-Generate tensor with all components equal to v h multilinearxGenerate tensor with random real components with given probability distribution. The tensor is wrapped in the IO monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Geometric : !Statistics.Distribution.Geometric  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace i multilinear{Generate tensor with random integer components with given probability distribution. The tensor is wrapped in the IO monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric j multilinear‚Generate tensor with random real components with given probability distribution and given seed. The tensor is wrapped in a monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Geometric : !Statistics.Distribution.Geometric  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace k multilinear…Generate tensor with random integer components with given probability distribution and given seed. The tensor is wrapped in a monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric e multilinear;Upper indices names (one character per index) and its sizes multilinear;Lower indices names (one character per index) and its sizes multilineardGenerator function (f [u1,u2,...] [d1,d2,...] returns a tensor element at t [u1,u2,...] [d1,d2,...]) multilinearGenerated tensorf multilinear;Upper indices names (one character per index) and its sizes multilinear;Lower indices names (one character per index) and its sizes multilineardGenerator function (f [u1,u2,...] [d1,d2,...] returns a tensor element at t [u1,u2,...] [d1,d2,...]) multilinearGenerated tensorg multilinear;Upper indices names (one character per index) and its sizes multilinear;Lower indices names (one character per index) and its sizes multilinearTensor elements value multilinearGenerated tensorh multilinear;Upper indices names (one character per index) and its sizes multilinear;Lower indices names (one character per index) and its sizes multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearGenerated tensori multilinear;Upper indices names (one character per index) and its sizes multilinear;Lower indices names (one character per index) and its sizes multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearGenerated tensorj multilinear;Upper indices names (one character per index) and its sizes multilinear;Lower indices names (one character per index) and its sizes multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated tensork multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated tensorefghijkefghjik<N-Vectors constructors (finitely- or infinitely-dimensional)(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_"l multilinear-Generate n-vector as function of its indices m multilinear/Generate n-vector with all components equal to v n multilinear|Generate n-vector with random real components with given probability distribution. The n-vector is wrapped in the IO monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Geometric : !Statistics.Distribution.Geometric  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace o multilinearGenerate n-vector with random integer components with given probability distribution. The n-vector is wrapped in the IO monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric p multilinear‚Generate n-vector with random real components with given probability distribution and given seed. The form is wrapped in a monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Geometric : !Statistics.Distribution.Geometric  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace q multilinear…Generate n-vector with random integer components with given probability distribution and given seed. The form is wrapped in a monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric l multilinear'Indices names (one characted per index) multilinear Indices sizes multilinearGenerator function multilinearGenerated n-vectorm multilinear'Indices names (one characted per index) multilinear Indices sizes multilinearn-vector elements value multilinearGenerated n-vectorn multilinear'Indices names (one character per index) multilinear Indices sizes multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearGenerated linear functionalo multilinear'Indices names (one character per index) multilinear Indices sizes multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearGenerated n-vectorp multilinearIndex name (one character) multilinearNumber of elements multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated n-vectorq multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated n-vectorlmnopqlmnpoq.N-Forms, dot and cross product and determinant(c) Artur M. Brodzki, 2018 GLP-3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_cer multilinear+Generate N-form as function of its indices s multilinear-Generate N-form with all components equal to v t multilinear|Generate n-vector with random real components with given probability distribution. The n-vector is wrapped in the IO monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Geometric : !Statistics.Distribution.Geometric  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace u multilinearGenerate n-vector with random integer components with given probability distribution. The n-vector is wrapped in the IO monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric v multilinear‚Generate n-vector with random real components with given probability distribution and given seed. The form is wrapped in a monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Geometric : !Statistics.Distribution.Geometric  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace w multilinear…Generate n-vector with random integer components with given probability distribution and given seed. The form is wrapped in a monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric x multilinear"2-form representing a dot product y multilinearTensor representing a cross product (Levi - Civita symbol). It also allows to compute a determinant of square matrix - determinant of matrix M9 is a equal to length of cross product of all columns of M r multilinear'Indices names (one characted per index) multilinear Indices sizes multilinearGenerator function multilinearGenerated N-forms multilinear'Indices names (one characted per index) multilinear Indices sizes multilinearN-form elements value multilinearGenerated N-formt multilinear'Indices names (one character per index) multilinear Indices sizes multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearGenerated linear functionalu multilinear'Indices names (one character per index) multilinear Indices sizes multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearGenerated n-vectorv multilinearIndex name (one character) multilinearNumber of elements multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated n-vectorw multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated n-vectorx multilinear'Indices names (one characted per index) multilinear/Size of tensor (dot product is a square tensor) multilinearGenerated dot producty multilinear'Indices names (one characted per index) multilinear/Size of tensor (dot product is a square tensor) multilinearGenerated dot productrstuvwxyrstvuwxy 9Matrix constructors (finitely- or infinitely dimensional)(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_¤Ăz multilinear+Generate matrix as function of its indices { multilinear-Generate matrix with all components equal to v | multilinearxGenerate matrix with random real components with given probability distribution. The matrix is wrapped in the IO monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace } multilinear{Generate matrix with random integer components with given probability distribution. The matrix is wrapped in the IO monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric ~ multilinear†Generate matrix with random real components with given probability distribution and given seed. The matrix is wrapped in the a monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace  multilinear†Generate matrix with random integer components with given probability distribution. and given seed. The matrix is wrapped in a monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric z multilineareIndices names (one character per index, first character: rows index, second character: columns index) multilinearNumber of matrix rows multilinearNumber of matrix columns multilinear3Generator function - returns a matrix component at i,j multilinearGenerated matrix{ multilineareIndices names (one character per index, first character: rows index, second character: columns index) multilinearNumber of matrix rows multilinearNumber of matrix columns multilinearValue of matrix components multilinearGenerated matrix| multilineareIndices names (one character per index, first character: rows index, second character: columns index) multilinearNumber of matrix rows multilinearNumber of matrix columns multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearGenerated matrix} multilineareIndices names (one character per index, first character: rows index, second character: columns index) multilinearNumber of matrix rows multilinearNumber of matrix columns multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearGenerated matrix~ multilineareIndices names (one character per index, first character: rows index, second character: columns index) multilinearNumber of matrix rows multilinearNumber of matrix columns multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated matrix multilineareIndices names (one character per index, first character: rows index, second character: columns index) multilinearNumber of matrix rows multilinearNumber of matrix columns multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated matrixz{|}~z{|~} DLinear functional constructors (finitely- or infinitely-dimensional)(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_Ýš€ multilinear2Generate linear functional as function of indices  multilinear=Generate linear functional with all components equal to some v ‚ multilinear‡Generate linear functional with random real components with given probability distribution. The functional is wrapped in the IO monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace ƒ multilinearŠGenerate linear functional with random integer components with given probability distribution. The functional is wrapped in the IO monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric „ multilinear‘Generate linear functional with random real components with given probability distribution and given seed. The functional is wrapped in a monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace … multilinear”Generate linear functional with random integer components with given probability distribution and given seed. The functional is wrapped in a monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric € multilinearIndex name (one character) multilinearNumber of elements multilinearDGenerator function - returns a linear functional component at index i multilinearGenerated linear functional multilinearIndex name (one character) multilinearNumber of elements multilinearValue of each element multilinearGenerated linear functional‚ multilinearIndex name (one character) multilinearNumber of elements multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearGenerated linear functionalƒ multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearGenerated linear functional„ multilinearIndex name (one character) multilinearNumber of elements multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated linear functional… multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated linear functional€‚ƒ„…€‚„ƒ… 9Vector constructors (finitely- or infinitely-dimensional)(c) Artur M. Brodzki, 2018 BSD3 artur@brodzki.org  experimental Windows/POSIX None &'17=>?@AX_† multilinear'Generate vector as function of indices ‡ multilinear2Generate vector with all components equal to some v ˆ multilinearxGenerate vector with random real components with given probability distribution. The vector is wrapped in the IO monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace ‰ multilinear{Generate vector with random integer components with given probability distribution. The vector is wrapped in the IO monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric Š multilinear‚Generate vector with random real components with given probability distribution and given seed. The vector is wrapped in a monad. %Available probability distributions:  Beta : (Statistics.Distribution.BetaDistribution  Cauchy : %Statistics.Distribution.CauchyLorentz Chi-squared : "Statistics.Distribution.ChiSquared Exponential : #Statistics.Distribution.Exponential Gamma : Statistics.Distribution.Gamma  Normal : Statistics.Distribution.Normal  StudentT :  Statistics.Distribution.StudentT  Uniform : Statistics.Distribution.Uniform F : %Statistics.Distribution.FDistribution  Laplace : Statistics.Distribution.Laplace ‹ multilinear…Generate vector with random integer components with given probability distribution and given seed. The vector is wrapped in a monad. %Available probability distributions:  Binomial :  Statistics.Distribution.Binomial  Poisson : Statistics.Distribution.Poisson  Geometric : !Statistics.Distribution.Geometric Hypergeometric: &Statistics.Distribution.Hypergeometric † multilinearIndex name (one character) multilinearNumber of elements multilinear9Generator function - returns a vector component at index i multilinearGenerated vector‡ multilinearIndex name (one character) multilinearNumber of elements multilinearValue of each element multilinearGenerated vectorˆ multilinearIndex name (one character) multilinearNumber of elements multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearGenerated vector‰ multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearGenerated vectorŠ multilinearIndex name (one character) multilinearNumber of elements multilinear-Continuous probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated vector‹ multilinearIndex name (one character) multilinearNumber of elements multilinear+Discrete probability distribution (as from Statistics.Distribution) multilinearRandomness seed multilinearGenerated vector†‡ˆ‰Š‹†‡ˆŠ‰‹ Safe&'17=>?@AX_Ý—˜™š›œžŸ !"# $%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abBCEFGHcdefghicefghicefghiXj c e f g h i c e f g h i c e f g h iklmnopqrstu v w x y z { | }~*multilinear-0.3.2.0-EJvOqjx3jDc9fqGrefa3sMMultilinear.IndexMultilinear.ClassMultilinear.Index.FiniteMultilinear.GenericMultilinear.Index.InfiniteMultilinear.TensorMultilinear.NVectorMultilinear.NFormMultilinear.MatrixMultilinear.FormMultilinear.Vector MultilinearPaths_multilinearTIndex Covariant Contravariant Indifferent indexSize tIndexNameIndex indexName isCovariantisContravariant isIndifferentequivI!=!toTIndex $fOrdTIndex $fShowTIndex $fIndexTIndex $fEqTIndex$fGenericTIndex Accessibleel$$|+.-.*..+.-.*indices indicesNamesordersizeequiv|==|$|raise/\lower\/ transpose shiftRight|>>shiftRightmost|>>> shiftLeft<<| shiftLeftmost<<<|mapfilter filterIndexzipWith indexName' $fNFDataIndex $fOrdIndex $fIndexIndex $fShowIndex $fEqIndex$fGenericIndexTensorScalar SimpleFinite FiniteTensor scalarValtensorFiniteIndex tensorScalars tensorsFiniteisScalarisSimpleisFiniteTensor tensorIndex! _standardize _elemByElemdotcontractionErr$fAccessibleTensora$fMultilinearTensora$fFloatingTensor$fFractionalTensor $fNumTensor $fShowTensor$fNFDataTensor $fEqTensor$fGenericTensor fromIndicesgenerateconst randomDouble randomIntrandomDoubleSeed randomIntSeedcrossincompatibleTypes scalarIndices indexNotFoundtensorOfScalars firstTensor _mergeScalars_map _elemByElem'zipTzipErr _transposeversion getBinDir getLibDir getDynLibDir getDataDir getLibexecDir getSysconfDirgetDataFileName